I have tried to understand how the change in potential energy is equal to the negative of the work done by gravity on a body in free fall.
If we were to consider a body of mass $m$ dropped from height $h_1$ to $h_2$ and try to use $E_g = -(U_f - U_i)$ where $W_g$ is the work done by gravity, $U_f$ is the final potential energy and $U_i$ is the initial potential energy, then:
In which Work done by gravity is clearly NOT EQUAL to the negative of the change in potential energy. Am I doing something wrong here?
However, if were to to consider the opposite motion of the body being lifed by us from height $h_2$ to $h_1$, $W_u$ is the work done by us, $U_f$ is the final potential energy and $U_i$ is the initial potential energy, then:
$$Wu=-(mg(h_1-h_2))$$ (We add negative sigh here since displacement is in the opposite direction of force applied by us.)
Here the statement 'Work done by gravity is the negative of the change in potential energy' holds true, but not in the first case. Please could you explain this.